# Recurrence Relation Q

• September 30th 2009, 06:11 PM
vuze88
Recurrence Relation Q
If $u_{n+1}=u_n+u_n^2$ and $u_1=\frac{1}{3}$, find $\sum_{n=1}^{\infty}\frac{1}{1+u_n}$.

So far, ive gotten up to $\sum_{n=1}^{\infty}\frac{1}{1+u_n}=\sum_{n=1}^{\in fty}\frac{u_n}{u_{n+1}}$ but im not sure whether im on the right track.

Can someone give me a hint on this one. Thanks
• September 30th 2009, 11:57 PM
malaygoel
$
\frac{1}{1+u_n}=\frac{1}{u_{n}}-\frac{1}{u_{n+1}}
$